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Current Attempt in Progress

Use the Taylor approximation for $x$ near $0,$

$cosx$~~$1-\frac{x^2}{2!}+\frac{x^4}{4!},$

to compute $\underset{x0}{lim}\frac{1-cosx}{5x^2}$

$\underset{x0}{lim}\frac{1-cosx}{5x^2}=$